Communications in Mathematical Sciences

Volume 17 (2019)

Number 5

Dedicated to the memory of Professor David Shen Ou Cai

Analysis of spike-driven processes through attributable components

Pages: 1177 – 1192



Horacio G. Rotstein (Federated Department of Biological Sciences and the Institute for Brain and Neuroscience Research, New Jersey Institute of Technology, Rutgers University, Newark, N.J., U.S.A.)

Esteban G. Tabak (Courant Institute of Mathematical Sciences, New York University, New York, N.Y., U.S.A.)


Postsynaptic neuron activity at both the sub and suprathreshold level is analyzed through the combination of: (1) the numerical simulation of a simple leaky integrate-and-fire model forced by both constant frequency and Poisson-distributed presynaptic spike-trains, (2) the transformation of the model’s response into sequences describing non-summation effects in subthreshold and the probability of spiking within a time-window in suprathreshold dynamics, (3) for constant frequency input, the analysis of these sequences through an autoregressive linear model, and (4) for non-uniform input, their analysis through attributable components. It is found that the attributable component methodology can reproduce the dynamics on testing data, effectively replacing the original dynamical model, and that the optimal order of both the autoregressive and the attributable component model, is an indicator of the relative strength of the underlying depression and facilitation mechanisms.


time series, history-dependent processes, synaptic short-term plasticity, dimensional reduction, attributable components

2010 Mathematics Subject Classification

37N25, 62-07, 62G08, 92C20

This work was partially supported by the National Science Foundation grants DMS-1608077 (HGR) and DMS-1715753 (EGT), by NIH MH060605 and by the Office of Naval Research (EGT).

Received 30 May 2018

Accepted 4 May 2019

Published 6 December 2019